1. Field of the Invention
The present invention relates to nuclear magnetic resonance (NMR) spectroscopy and, more particularly, to NMR spectrometer probes which can generate a magnetic field gradient along the axis of a sample being rotated at the "magic angle."
2. Description of the Related Art
All atomic nuclei with an odd atomic mass or an odd atomic number possess a nuclear magnetic moment. Nuclear magnetic resonance (NMR) is a phenomenon exhibited by this select group of atomic nuclei (termed "NMR active" nuclei), and is based upon the interaction of the nucleus with an applied, external magnetic field. The magnetic properties of a nucleus are conveniently discussed in terms of two quantities: the gyromagnetic ratio (.gamma.); and the nuclear spin (I). When an NMR active nucleus is placed in a magnetic field, its nuclear magnetic energy levels are split into (2I+1) non-degenerate energy levels, which are separated from each other by an energy difference that is directly proportional to the strength of the applied magnetic field. This splitting is called the "Zeeman" splitting and is equal to .gamma.hH.sub.o /2.pi., where h is Plank's constant and H.sub.o is the strength of the magnetic field. The frequency corresponding to the energy of the Zeeman splitting (w.sub.o =.gamma.H.sub.o) is called the "Larmor frequency" and is proportional to the field strength of the magnetic field. Typical NMR active nuclei include .sup.1 H (protons), .sup.13 C, .sup.19 F, and .sup.31 P. For these four nuclei I=1/2, and each nucleus has two nuclear magnetic energy levels.
When a bulk sample containing NMR active nuclei is placed within a magnetic field, the nuclear spins distribute themselves amongst the nuclear magnetic energy levels in accordance with Boltzmann's statistics. This results in a population imbalance between the energy levels and a net nuclear magnetization. It is this net nuclear magnetization that is studied by NMR techniques.
At equilibrium, the net nuclear magnetization is aligned parallel to the external magnetic field and is static. A second magnetic field perpendicular to the first and rotating at, or near, the Larmor frequency can be applied to induce a coherent motion of the net nuclear magnetization. Since, at conventional field strengths, the Larmor frequency is in the megahertz frequency range, this second field is called a "radio frequency" or RF field.
The coherent motion of the nuclear magnetization about the RF field is called a "nutation." In order to conveniently deal with this nutation, a reference frame is used which rotates about the z-axis at the Larmor frequency. In this "rotating frame" the RF field, which is rotating in the stationary "laboratory" reference frame, is static. Consequently, the effect of the RF field is to rotate the now static nuclear magnetization direction at an angle with respect to the main static field direction. By convention, an RF field pulse of sufficient length to nutate the nuclear magnetization through an angle of 90.degree., or .pi./2 radians, is called a ".pi./2 pulse."
A .pi./2 pulse applied with a frequency near the nuclear resonance frequency will rotate the spin magnetization from an original direction along the main static magnetic field direction into a plane perpendicular to the main magnetic field direction. Because the RF field and the nuclear magnetization are rotating, the component of the net magnetization that is transverse to the main magnetic field precesses about the main magnetic field at the Larmor frequency. This precession can be detected with a receiver coil that is resonant at the precession frequency and located such that the precessing magnetization induces a voltage across the coil. Frequently, the "transmitter coil" employed for applying the RF field to the sample and the "receiver coil" employed for detecting the magnetization are one and the same coil.
In addition to precessing at the Larmor frequency, in the absence of the applied RF energy, the nuclear magnetization also undergoes two relaxation processes: (1) the precessions of various individual nuclear spins which generate the net nuclear magnetization become dephased with respect to each other so that the magnetization within the transverse plane loses phase coherence (so-called "spin-spin relaxation") with an associated relaxation time, T.sub.2, and (2) the individual nuclear spins return to their equilibrium population of the nuclear magnetic energy levels (so-called "spin-lattice relaxation") with an associated relaxation time, T.sub.1.
The nuclear magnetic moment experiences an external magnetic field that is reduced from the actual field due to a screening from the electron cloud. This screening results in a slight shift in the Larmor frequency (called the "chemical shift" since the size and symmetry of the shielding is dependent on the chemical composition of the sample).
Since the Larmor frequency is proportional to the field strength, it is generally desirable to insure that the main magnetic field and the RF magnetic field are spatially homogeneous, at least in the sample area, so that all parts of the sample generate an NMR signal with the same frequency. However, there are some known applications of NMR techniques for which it is desirable to establish a magnetic field gradient across the sample: examples of such applications include NMR imaging, molecular diffusion measurements, solvent suppression, coherence pathway selection and multiple-quantum filters.
A conventional method of applying such gradients is to use special gradient coils in addition to the coils which generate the main static field and the coils which generate the RF magnetic field. These special coils are located in the NMR probe and generate a magnetic field gradient called a B.sub.o gradient which has at least one field component that has a direction parallel to the main static field direction, but has an amplitude which varies as a function of spatial position. All of the aforementioned NMR applications have been demonstrated utilizing a B.sub.o gradient. The coils which generate the B.sub.o gradients along the Cartesian axes are well-known.
Many samples of solids or gels display rather broad NMR resonances when measured via liquid state NMR methods since the molecules are not free to tumble rapidly and isotropically. These additional broadenings arise from dipole-dipole interactions between spins, the anisotropy of the chemical shift and local variations in the magnetic susceptibility. Magic angle sample spinning (MAS) is a well-known means of restoring the spectra to a seemingly high resolution result by introducing a physical rotation of the sample as a whole about the so-called magic angle, .theta..sub.m, to the static field direction, where cos .theta..sub.m =.sqroot.1/3. This angle corresponds to the bisector of a cube (along the 1,1,1! direction relative to an x,y,z Cartesian coordinate system), and rotation about this axis creates an equal weighting of evolution for the x, y, and z directions, averaging out the local variations. Provided that the spinning rate is fast compared to the line width, sharp resonances are observed in MAS experiments. Spinning rates of from 2 to 10 kHz are routinely achieved in MAS probes.
For certain solid state imaging experiments, gradient coils have been used with MAS probes to create a rotating imaging reference frame which, relative to the sample, appears stationary. This differs from the conventional reference frame which is actually fixed, and within which the sample is rotating relative to the reference frame at the above-mentioned spinning rate. In all of the approaches to creating such a modified reference frame, the gradient fields were caused to rotate synchronously with the sample by modulating the currents through specially designed gradient coils. In order to use three gradient sets to generate a .differential.B.sub.z /.differential..theta..sub.m field, a full set of three gradient coils is required, each with its own audio amplifier. The coils are driven by a carefully tuned oscillator circuit that must be phase-locked to the position of the sample. This high degree of complexity is essential for imaging when all three spatial axes are used, but is more than needed for spectroscopy.
In another prior art design, a set of gradient coils has been implemented that creates a gradient field oriented along the magic angle by creating a complex current distribution on a cylinder oriented along the static field. This arrangement was proposed to avoid interferences from dipolar demagnetizing fields and was not designed to operate with a MAS probe. It has the gradient coils wrapped on a cylinder oriented along the main magnetic field direction. This method suffers from a number of difficulties. First, the arrangement would have to take up space which is required for the MAS stator. Secondly, the gradient coil must be precisely aligned with the spinner axis and, with the gradient coil and the stator as two separate pieces, alignment of the two pieces must be performed for each probe. Also, the gradient coil can interfere with the ejection of the sample container.
When implementing gradient spectroscopy experiments in a MAS probe, it would be desirable to have a gradient design in which the gradient is oriented such that the z-component of the magnetic field increases along the axis of the spinner, and the gradient magnetic field is uniform in the planes perpendicular to the spinner axis. It would also be desirable to have a gradient field which is obtained for a DC current through the gradient winding, and for which no synchronization to the spinner motion is necessary. Furthermore, it would be advantageous if such a design was compatible with the mechanical layout of prior-art MAS stator designs, did not interfere with sample insertion/ejection, and had a gradient strength of conventional strength (on the order of 50 G/cm)